Transcription
Welcome back to Science Click. Today, the geometry of colors. In a drawing or photography software, you've probably already encountered a color picker; a space allowing the user to choose a color. Some pickers are square, others round or triangular. Some colors are shown close together, others far apart. But is there a link between these representations? Can we make sense of the distances in these spaces? Is there an underlying geometry to describe all colors?
In this video, we will explore these questions which have occupied thinkers from Aristotle to Schrödinger, including Maxwell and Goethe, at the crossroads of physics, biology, mathematics, and psychology. Let's dive together into the science of colors.
[Music]
To begin with, what is a color? Contrary to what one might think, objects do not have an intrinsic color. Colors are feelings, subjective perceptions created by our brain when our eyes receive light. The light from the sun, for instance, is a wave, which can be interpreted as the sum of several waves with different lengths, like the different notes that make up a music chord. Objects absorb some of these waves and reflect others. This apple, for example, contains pigments in its skin which absorb short waves and reflect long waves. Our eyes are sensitive to these different wavelengths, and they transmit a signal to the brain which gets interpreted as the sensation of color red in this case.
To tackle the problem in order, let's start by focusing on light.
[Music]
We can decompose sunlight using a glass prism. The waves interact with the atoms and are diverted differently depending on their length. We thus observe the individual color of each wavelength. These are the colors of the rainbow because raindrops behave somewhat like tiny prisms, and they range from red to blue-violet through yellow, green, and cyan. This is our first color space, the visible spectrum; a one-dimensional space that contains all pure colors, those corresponding to a single wavelength. In reality, there are other waves on either side of the spectrum, infrared and ultraviolet, but our eyes do not detect them.
As early as 1666, Newton understood that the white light from the sun results from a mixture of all hues of the spectrum. We can now play around by testing other mixtures. Red and yellow make orange. Green and blue make cyan. These are new colors because they are slightly different from those of the spectrum, less pure, closer to white. By mixing the colors of the spectrum with each other, we construct a brand new dimension, saturation. It measures the extent to which colors are vibrant, close to the spectrum. Please note that when we talk about mixtures in this video, we are referring to mixtures of light when we superimpose them. This is additive color synthesis. Each light adds new waves to the mixture. In contrast, mixtures of paints or dyes work by subtraction. They absorb waves from the light that illuminates them. These mixtures are more complex to describe because they depend on the chemical composition of the pigments as well as the surrounding light. We can forget about them for the rest of the video.
Rather than organizing the colors like this pyramid, Newton proposes a new geometry. He decides to close the diagram on itself to make a circle, placing white at the center. The idea is that when we mix two lights, the resulting color would be located, according to Newton, halfway between the two points. Red and yellow make orange. Green and blue make cyan.
[Music]
Color mixtures can thus be predicted geometrically. Complimentary colors can be found on either side of the center. They add up to white. Yellow and indigo, for instance. To connect the two ends of the spectrum, we have to introduce new hues opposite to green, purples. They correspond to mixtures of red and blue-violet. These hues do not exist in the spectrum. They can only be obtained by mixing at least two wavelengths, one from each end. They form a transition between blue and red. Finally, if we vary the intensity of the light, we can produce all the intermediate shades from white to black, like gray or brown, which are dark white and dark orange. With this third axis, we finally have a complete space that takes the shape of a cone and describes all colors. In this abstract space, properties of colors become geometric: hue, brightness, saturation. A simple and a useful model.
[Music]
Up until the 20th century, other geometries were proposed: spheres, triangles, cubes, double cones, each with advantages and disadvantages. Effectively, Newton's circle was only an approximation and presents a number of problems. For example, red and yellow don't produce this pale orange, but an almost pure orange closer to the spectrum. Another problem: within the spectrum, our eyes are more sensitive to medium wavelengths, which is why yellow appears brighter than indigo. Different hues have different intensities for our eyes. And if we adjust the diagram so that the intensity is uniform, certain mixtures are no longer correct. Yellow and indigo, for instance, only give white if we add more yellow than indigo.
It was Helmholtz who would eventually fix these issues by distorting the diagram. The curve linking red and yellow should be almost flat because their mixture is close to the spectrum. Indigo should be further away from white than yellow because it takes more yellow than indigo to produce white. Finally, purples should lie on a straight line, not a curve, as they correspond to the progressive mixtures between the two ends of the spectrum. In this way, Helmholtz obtained a horseshoe-shaped diagram.
In 1931, the International Commission on Illumination defined an improved version of this space which would become the standard for describing colors. The XYZ space, a mathematical space in which colors can be added like vectors to calculate mixtures. In theory, this space extends to infinity for arbitrarily intense lights. But if we restrict ourselves to a maximum energy for each wavelength, we obtain a finite volume, the optimal solid. This object theoretically contains all colors that can be observed up to a certain luminosity. It presents on its boundary the most vivid shades possible of each hue. Black is connected to white by two sharp edges: black, red, yellow, white, and white, cyan, blue, black. Gradients that we can observe near a prism where the wavelengths are not fully separated. Artists call these warm and cool colors.
[Music]
Let's open a parenthesis. The colors that are currently displayed are not entirely accurate for several reasons. First, your surroundings affect your perception of colors, whether it's day or night, for instance. Second, your monitor can't produce all colors. It works by mixing lights of three primary colors for each pixel, usually red, green, and blue. Depending on the intensity of these three lights, the screen can synthesize colors within a triangle or a cube in three dimensions. This is the sRGB space. These colors are enough for most images, but we do miss some very vivid ones, such as those we see during a sunset. Finally, even under identical conditions, we don't all perceive the same colors. On the one hand, there are psychological factors that affect perception. On the other, some of us are colorblind. Several conditions that affect 5% of the population, mainly men, for genetic reasons.
To differentiate colors, our eye uses three receptors or cones scattered across the retina. They each react to one of three ranges of wavelengths corresponding very roughly to the red, green, and blue components of light. Our brain constructs the colors we perceive from these three signals. And this is why the space of colors systematically has three dimensions: red, green, blue or hue, saturation, brightness. However, colorblind people have deficiencies in the retina or visual system. So the space they perceive is reduced. Depending on which receptors are affected, there are several types of color blindness, each with their own color space, sometimes spanning only two or even a single dimension.
At the dawn of the 20th century, psychologist and mathematician Christine Ladd-Franklin proposed that color vision appeared gradually over the course of evolution. The first eyes distinguished only one dimension between light and dark. A second dimension then appeared, allowing us to differentiate long from short waves, yellow from blue. Finally, a third dimension differentiates long from medium waves, red from green. Our distant ancestors also perceived a fourth dimension in the ultraviolet, which many animals have retained to this day. But mammals would have lost two of these dimensions, forced to hide under the reign of the dinosaurs. Even today, a tiger is still perfectly camouflaged in the eyes of its prey, which can only perceive two dimensions. In humans and certain primates, the third dimension of color has reappeared more recently. That said, there are also a few tetrachromatic humans with a fourth cone between red and green, particularly some women in northern England. Researchers are interested in whether they actually perceive a differently colored world from our own.
[Music]
Until now, we have organized colors according to physical criteria based on light and mixtures. But while these diagrams are useful mathematically, they do not reflect how we perceive colors from a sensory point of view. Blue or yellow hues, for instance, seem more compressed than green ones. The distances in the diagram have nothing to do with our perception of the differences between colors. Some are far apart while they appear similar.
While preparing this video, I asked for your help to try to measure this effect. A huge thank you as we collected tens of thousands of responses for the experiment. The goal was to determine at what distance in the diagram we can no longer distinguish two colors. I asked you to play a game in which you had to identify which of the three colors was different from the other two by repeating the operation with different combinations of colors on more than a million samples. The results of the test enable us to plot a set of ellipses which represent regions in which the colors are statistically indistinguishable for our eyes. They all differ in size and orientation which indicates that the diagram is not faithful to our perception of the differences between colors. For instance, around blue, it's easier to distinguish colors in this direction than in this one. This was actually a crude reproduction of a famous experiment carried out by David MacAdam in 1942.
Thus, in parallel to the physical approach, another approach was developed: the psychological approach. Some like Goethe or Hering sought to organize colors directly from sensations. According to them, our perception is based on fundamental oppositions between black and white, red and green, yellow and blue. A theory that is now considered valid because certain cells in the retina actually transform the red, green, and blue signals into signals of oppositions based on precise measurements of color perception. Some constructed detailed atlases such as the famous Munsell system from the early 20th century. Its irregular geometry closely models our perceptions of different hues. We note that different hues reach their maximum saturation at different brightness levels. Some colors, such as yellow, tend to appear lighter than others, such as blue. Some hues also tend to appear more vivid than others, such as magenta, compared to turquoise.
During this period, psychophysics also appeared which attempts to mathematically link our sensations to the physical stimuli which provoke them. Let's take a black and white gradient. It is linear. The intensity increases by a constant amount from one slice to the next. However, the variation seems stronger in the dark areas than in the light areas on the right. This is the Weber-Fechner law. A small variation in intensity is better perceived when the overall intensity is low. We can model this effect with a mathematical function which represents our perception of brightness as a function of the actual physical luminance of the light. We see that our perception is nonlinear. Brightness appears to increase quicker in dark areas. Taking this effect into account, we can create a more perceptually uniform gradient. And if we do this for each of the three dimensions of the color space, we obtain a more uniform distribution of colors. Gradients appear smoother and more regular than in the basic color space. This is the founding principle of the Lab space defined in 1976 by the International Commission on Illumination. It is inspired by the psychological interpretation of colors and opposes black and white, red and green, yellow and blue.
In 2020, Björn Utson proposed the OKLab space as a more precise alternative. Its geometry resembles a deformed droplet or an inclined double cone designed to model the distances we perceive between colors. This section corresponds to the colors that a standard screen can display. Finally, here's what a color picker looks like in the OKLab space compared to a traditional one.
Today, new mathematical spaces and models are used to describe colors more accurately than ever before. They can help artists select colors more perceptually, but also scientists to construct color codes to visualize data. The study of perception is important for designing more faithful screens and making certain content accessible to colorblind people. This text, for instance, if we vary its hue, becomes more or less readable in the basic color space. But in a perceptual space like OKLab, this problem disappears because this space better represents our perception of colors. However, no model is perfect, and color remains an active area of research. Some, like Schrödinger in the early 20th century, believe that the color space is described by a non-Euclidean curved geometry, much like spacetime in general relativity. Others proposed that the color space is even more complex to describe, requiring the development of a completely new type of geometry.
To conclude, in April 2025, a research team claimed to have produced a completely new color. As we have seen, our retina has three types of receptors, each sensitive to a range of wavelengths, long, medium, and short. But these ranges overlap in places. In particular, the medium cone is never activated on its own. There is no wavelength that only activates this receptor without also activating one of the other two. In this study, the scientists were able to stimulate the medium cones only using extremely precise lasers directly targeting the concerned cells. The researchers would have thus produced a brand new sensation named OLO. This new color would be located outside the usual space. Participants say they observed an extremely intense shade of turquoise.
[Music]